One-step hologram (including holographic stereogram) production technology has been used to satisfactorily record holograms in holographic recording materials without the traditional step of creating preliminary holograms. Both computer image holograms and non-computer image holograms may be produced by such one-step technology. In some one-step systems, computer processed images of objects or computer models of objects allow the respective system to build a hologram from a number of contiguous, small, elemental pieces known as hologram elements or hogels. To record each hogel on holographic recording material, an object beam is conditioned through the rendered image and interfered with by a reference beam. A number of hogels recorded together on the same piece of holographic recording material is often referred to as a tile. Examples of techniques for one-step hologram production can be found in the U.S. Pat. No. 6,330,088 entitled “Method and Apparatus for Recording One-Step, Full-Color, Full-Parallax, Holographic Stereograms,” Ser. No. 09/098,581, naming Michael A. Klug, Mark E. Holzbach, and Alejandro J. Ferdman as inventors, and filed on Jun. 17, 1998 (“the '088 patent”), which is hereby incorporated by reference herein in its entirety. Two-step holograms are created using indirect or transfer methods, that require recording a transfer hologram before recording the master hologram.
FIG. 1A illustrates the relationship between a hogel 120 and the computer graphics image 130 used to create the hogel (this relationship is similar to the relationship among hologram recorder components such as a spatial light modulator and holographic recording material, as discussed below). The computer graphics image 130 is made up of a number of pixels 140 each of which can have data values depending on, for example, color and intensity. Each of the pixels 140 can define a directional image sample through the hologram. As illustrated by arrows 150 and 160, the relative position of each pixel 140 with respect to hogel 120 can be used to define directions in which a three-dimensional (3D) computer graphics scene can be viewed and/or rendered.
Similarly, two elements of a hologram production system 100 are shown in FIG. 1. Spatial light modulator (SLM) 135 includes a number of pixels 140 upon which a computer graphics image can be displayed. An object beam (not shown) passes through spatial light modulator 135, which modifies the intensity of the object beam according to values of the various pixels 140. This object beam typically passes through optics (not shown) so that when the object beam reaches tile 110, it can be used in conjunction with a reference beam to form an interference pattern which is recorded as hogel 120.
FIG. 1B illustrates a the displaying of or “playback” of hogel 120. Light source 170 illuminates tile 110 causing the diffraction pattern recorded in hogel 120 to diffract the incident light as diffracted rays 155 and 165. The light diffracted by hogel 120 produces image 180.
Distortion associated with the generation of hogels for horizontal-parallax-only (HPO) holographic stereograms is analyzed Michael W. Halle in The Generalized Holographic Stereogram, Master's Thesis, Massachusetts Institute of Technology, February 1991, which is hereby incorporated by reference herein in its entirety. In general for HPO holographic stereograms, the best viewer location where a viewer of a holographic stereogram can see an undistorted image is at the distance where the camera (or the camera model in the case of computer graphics images) captured the scene. This is an undesirable constraint on the viewability of holographic stereograms. Using several different techniques, one can compensate for the distortion introduced when the viewer is not at the same distance with respect to the hologram as the camera. However, the geometry of both image creation/capture and the recording process means that such distortion compensation typically implies a single preferred viewing distance.
An anamorphic physical camera can be created with a standard spherical-surfaced lens coupled with a cylindrical lens, or alternately two crossed cylindrical lenses can be used. Using these optics, one can independently adjust horizontal and vertical angles used in acquiring the stereogram images, thereby avoiding distortion. Such physical systems are typically large, expensive devices that can require constant readjustment throughout the hologram production process. For these and other reasons, anamorphic optics are typically used to correct for distortion in holographic stereogram production, rather than in image acquisition.
Since the source of the images used for producing a holographic stereogram are typically rendered computer graphics images (or digital photographs), correcting the distortion as part of the image generation process is a common technique. For example, if the computer graphics images being rendered can be rendered as if seen through the aforementioned physical optics (e.g., using ray tracing where the computer graphics model includes the optics between the scene and the computer graphics camera), then hogel images that account for distortion can be directly rendered. However, such an application of ray tracing is currently impractical given the speed of software ray-tracers, the expense of hardware ray-tracers, and the size of the data sets typically involved in holographic stereogram production.
Another technique for rendering hogel images that are “pre-distorted” is described in M. Halle and A. Kropp, “Fast Computer Graphics Rendering for Full Parallax Spatial Displays,” Practical Holography XI, Proc. SPIE, vol. 3011, pages 105-112, Feb. 10-11, 1997, which is hereby incorporated by reference herein in its entirety. While useful for its speed, the techniques of Halle and Kropp often introduce additional (and undesirable) rendering artifacts and are susceptible to problems associated with aliasing. Improvements upon the techniques of Halle and Kropp are discussed in the U.S. patent entitled “Rendering Methods For Full Parallax Autosteroscopic Displays,” Ser. No. 09/474,361, naming Mark E. Holzbach and David Chen as inventors, and filed on Dec. 29, 1999, which is hereby incorporated by reference herein in its entirety.
Still another technique for rendering hogel images utilizes a computer graphics camera whose horizontal perspective (in the case of horizontal-parallax-only (HPO) and full parallax holographic stereograms) and vertical perspective (in the case for full parallax holographic stereograms) are positioned at infinity. Consequently, the images rendered are parallel oblique projections of the computer graphics scene, i.e., each image is formed from one set of parallel rays that correspond to one “direction”. If such images are rendered for each of (or more than) the directions that a hologram recorder is capable of recording, then the complete set of images includes all of the image data necessary to assemble all of the hogels. Note that in some cases, e.g., because of resolution or speed concerns, it may be desirable to render images for fewer than the number of directions that a hologram recorder is capable of recording. Additionally, when the depth of a scene is relatively shallow it may also be desirable to render fewer directional images than a hologram recorder is capable of recording—because in that case a lower number of directions may be sufficient, i.e., rendering more directions would not yield any improvement or noticeable effect in the final display.
Returning to FIG. 1A as an example, if each line between the center of each pixel 140 and the center of hogel 120 defines a direction (e.g., directions 150 and 160), then parallel oblique projections can be rendered (using image-based rendering or other techniques) for each direction. Each image resulting from the rendering represents a single direction, and includes a data value (e.g. a pixel intensity) for each hogel in tile 110. Consequently, the information needed to record any one hogel is distributed across a number of images. For example, the first pixel value of the first hogel of the tile is in the first image, the second pixel value for the first hogel is in the second image, the third pixel value for the first hogel is in the third image, and so on. Thus, image data must be rearranged to form hogels. Some techniques for rearranging or reparameterizing such data are described in the aforementioned master's thesis The Generalized Holographic Stereogram. Other techniques are described in the aforementioned '814 application.
The examples of FIGS. 1A and 1B assume that the rendering, recording, and displaying directions (as illustrated by 150, 155, 160, and 165) can be defined based on a simple geometric relationship between the pixels 140 of spatial light modulator 135 and the recording surface. However in practice, it has been observed that despite careful attention to rendering and recording in these directions, the holograms created can still exhibit various types of distortion. One example of that distortion is illustrated in FIG. 2. Regular grid 200 is shown in FIG. 2 and represents the desired image to be recorded in a hogel. Consequently, a computer graphics image of regular grid 200 is used as the image provided to a spatial light modulator that is part of a hogel recording system. Distorted grid 210, in this case illustrating pin-cushion distortion, is the resulting image upon play-back of the hogel based on regular grid 200. Thus, despite rendering the image of regular grid 200 according to directions defined by the relationship between SLM pixels and the recording surface, the play-back image is distorted. Unfortunately, the sources of distortion can be numerous and difficult to characterize, e.g., differences between the actual geometry of the hologram recorder and the model of FIG. 1A, optical elements located between the SLM and the recording material, recording material processing effects (e.g., material shrinkage), and display issues (e.g., location and type of light source, mounting of the hologram).
Additionally, the geometry of production systems, e.g., hologram recording devices, is typically much more fixed or constrained, and thus less adjustable, than computer based image acquisition systems. Consequently, it is generally more desirable to compensate for the problems described above at the acquisition stage rather than at a stage where hogels are recorded in a holographic recording material.
Accordingly, it is desirable to have image processing and hologram recording techniques that reduce or eliminate such distortions as part of the production of holographic stereograms.